def known_solutions(potential_min, potential_max, csv_path=None):
"""Returns [potential, stationarity, *coords] rows for known solutions."""
if csv_path is None:
csv_path = os.path.join(os.path.dirname(__file__),
'../equilibria/SO8_SOLUTIONS.csv')
return [numpy.asarray(row) for row in mu.csv_numdata(csv_path)
if potential_min <= row[0] <= potential_max]
def test_known_so8_solutions(self):
"""Asserts numpy stationarity of the known SO(8) solutions."""
for row in mu.csv_numdata('dim4/so8/equilibria/SO8_SOLUTIONS.csv'):
table_potential = row[0]
potential, stationarity = SUGRA.potential_and_stationarity(row[2:])
self.assertTrue(0.0 <= stationarity <= 1e-15)
self.assertTrue(numpy.isclose(potential, table_potential, atol=1e-8))
def test_known_so8c_solutions(self):
"""Asserts numpy stationarity of the known SO(8)c omega=pi/8 solutions."""
tc_omega = mu.tff64(numpy.pi / 8)
for row in mu.csv_numdata('dim4/so8/equilibria/SO8C_PI8_SOLUTIONS.csv'):
table_potential = row[0]
potential, stationarity = SUGRA.potential_and_stationarity(
row[2:], t_omega=tc_omega)
self.assertTrue(0.0 <= stationarity <= 1e-7)
self.assertTrue(numpy.isclose(potential, table_potential, atol=1e-8))
def demo_show_physics_so7():
"""Text-prints the physics of the known 'SO(7)+' solution."""
sugra = SO8_SUGRA()
rows = list(itertools.islice(mu.csv_numdata(
'dim4/so8/equilibria/SO8_SOLUTIONS.csv'), 10))
# phys = sugra.get_physics(rows[4][-70:],
# dict(name='some_solution')) # SU(3)xU(1) N=2
# phys = sugra.get_physics(rows[8][-70:], dict(name='SO(3)xSO(3) S0880733'))
phys = sugra.get_physics(rows[1][-70:], dict(name='SO(7)+'))
print(sugra.show_physics_text(phys))
verbosity='SF')):
sol = nn, pot, stat, *params.tolist()
sols.append(sol)
print(f'### nn={nn} P={pot:.8f} S={stat:.6g}\n')
with open(scan_file, 'at') as h_out:
print(','.join(map(repr, sol)), file=h_out)
if mu.arg_enabled(__name__, 'analyze_u4xr12_scan'):
# A deeper scan would reveal 24 different critical points.
# There might be more.
stationarity_limit = 1e-14
theta_sugra = gaugings.Dim4SUGRA(
get_theta_u4xr12(c=1.0),
gaugeability_atol=1e-10)
scanned = list(mu.csv_numdata(scan_file))
analyzed = {}
for row in scanned:
num_row = int(row[0])
if num_row % 10 == 0:
print(f'Row {num_row}...')
if row[2] > stationarity_limit:
continue # Skip bad data.
m_grav = theta_sugra.gravitino_masses_from_position(row[-70:])
key = f'{row[1]:.6f}'
analyzed.setdefault(key, []).append(
(num_row, ' '.join(f'{m:+.4f}' for m in m_grav)))
with open(analyzed_file, 'wt') as h_out:
h_out.write(pprint.pformat(analyzed, width=120))